Log-log duplex slide rule



April 1 1924.

A. W. KEUFFEL LOG LOG DUPLEX S LIDE RULE" Filed June 6, 1.922

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5 e tot Patented Apr. 1, 1924.

UNITED STATES 1,488,686, PATENT QFFICE.

ADOLF W. KEUFFEL. OF MONTCLAIR TOWNSHIP. ESSEX COUNTY, NEW JERSEY,y AS- SIGNOR T0 KEUFFEL & ESSER COMPANY, OF HOBOKEN, NEW JERSEY, A CORPORAL TION OF NEW JERSEY.

LOG-LOG DUPLEX SLIDE RULE.

Application led .Tune 8, 1922. Serial No. 566,340.

T0 all 'whoml 'it 91mg/ conce/vt.'

Be it known that I, Anota V. Kni'irrnr., a citizen of the United States, residing at 7 63 Bloonilield Avenue, in the township of Montclair, in the county of Essex and State 0f New Jersey, have invented certain new and useful ln'iprovcinents in Log-Lo Duplex Slide Rules, of which the following is a specification.

My invention relates to slide rules, and more particularly to a log log duplex slide rule, and the novelty consists of the construction adaptation and arrangement of tl1c` parts as will be more fully hereinafter pointed out.

The use of slide rules in many lines of business as well as professions has increased rapidly With the demand for quick and accurate solution of mathematical problems because the processes of businessl have changed, whereby instead of leaving the solution of such problems to the convenience of a corps of poorly paid clerks such prob lems are now solved immediately by the use of suitable slidc rules adapted for the particular purpose required. kThis has result-cd 'in the development and marketing of a large .number of different types of slide rules adapted for many dillercnt purposes, but never has there been a slide rule especially adapted for figuring fractional powers and roots whereby such problems may be solved directly on the rule.

My slide rule solves this problem and furnishes a means of solving problems involving decimal quantities directly by the use of a decimal logarithmic scale and without the. use of reciprocals.

Referring to the drawings Figure l is a top plan view of my slide rule; and Figure 2 is a top plan view of the reverse sideof my slide rule. v

In the drawings bars H and J are rigidly secured together by means of plates K which are riveted thereto at M, so that a, sliding bar N may be mounted between said bars H and J so as to be readily slidable longitudinally thereof. The slidable bar N has the usual tonfnie members on each-edge adapted to slide in the usual groove 'members on the edges of the bars H and J contiguous to the sliding bar B so that the sliding bar N is always held in engagement betweenv the bars H and J in Whatever position it occupies longitudinally thereof. A

Reissue) runner or indicator X, transparent on both faces and of usual construction, is mounted over said bars H, J and N so as to be readily moved into any position desired between the plates K, and the runner X has a hairline Y on each side thereof.

` On the front of my slide rule as shown in Figure 1, the upper scale on the bar H is designated as LL() and gives the graduated log-log fractional or decimal readings from .05 to .97. The next scale on the bar H is designated as A and contains the standard graduated logarithmic scale of two unit lengths from l to l0. The upper scale on the sliding bar N is designated as B, and has the saine graduation as the scale A. on the bar H. A second scale on the sliding bar N is designated as S, and has a graduated sine scale of degrees and minutes from 34 to 00o and is used with reference to scales A and ll. The third scale on the sliding bar N is designated as T and has a graduated standard tangent scale with divisions from 4.3 to 45o. The fourth scale on the sliding bar N is designated as C and has standard graduated logarithn'iic divisions of full unit lengt-h from l to 10. The upper scale on thc bar .l is designated as Ll, and has log log graduations from 2.7 to 20,000. The second scale on the bai' J is designated as LLQ., and has log log graduations from 1.105 to 2.7. The third scale on the bar J isl designated as LLl, and has log log gradu ations from 1.01 to 1.105.

On the back of my slide rule, as shown in Figure 2, the scale shown on bar J is desiguated as D F, and is a standard logarithn mic scale of full unit length the same as the C scale described above, except that it is folded and has its index at the centre. The upper scale on the sliding bar N is designated as C F, and is identical with the scale D F on bar J The second scale on the sliding N is designated as CI and is a standard reciprocal logarithmic scale of full unit length graduated from l0 to l. The third scale on the sliding bar N is designated as C and is a standard logarthmic scale of full unit length identical with C scale above described. The first scale on the bar H is designated as D, and is the same as the scale C on the sliding bar N. The second scale on the bar H is designated as L and is a scale of equal parts from 0 to lO, and is used to obtain common logarithms when referred to scale D.

As has been above stated there have been log log slide rules on the market for some time. and with these log log slide rules it is possible to solve problems involving tractional powers and roots as well as natural or hyperbolic logaritlnnjs. These log log slide rules of the prior art had graduated logarithmic scales designed as LLI. LLQ and LLB, the same` as illustrated herein.

On these slides rules embodying the logarithmic scales mentioned it was not possible to handle decimal or fractional roots and powers directly, as the reciprocal ot the quantity must be first taken thereon, and this reciprocal then evaluated in the integralscalcs and then the reciprocal of the result taken in order to get the required answer. This operation involved a number of additional operations, both mentally and mechanically, and increased the liability ot error, as the correctness ct the result depended not on the mechanical operation of the slide rule alone, but also upon the mental operation of the operator combined with the mechanical operation of the slide rule.

illy slide rule has overcome this ditiiculty and made it possible to handle decimal or fractional roots and powers so as to obtain the solution ot` examples in formulas involving fractional powers and roots direct ly on my slide rule by mere mechanical operation ot the same and Without the use .ot reciprocals @t the quantities handled, thereby eliminating any separate mental operation and the possibility of errors involved therein.

In the equation of the catenary curve and in hyperbolic functions, the expression eVX occurs. in which 6:17152* is the base ot natural or Napierian logarithms.y also in many formulas the logarithms to base he is required or is to be taken as a factor.

By placing the reciprocal of e on scale LL() in alignment With an index l of the regular logarithmic scale A. the values ot e can be at once read for all values of ai within the range ot the scale, without the setting of the slide N and also the cologarithms to base e can be directly read on A.

In order to make this clearer I will give a few examples, showing the old method as heretofore used and showin;- how to .solve the problems by the new method.

Example 1.

Bequired @$20.85.

By the old method it is necessary to set the runner or indicator to .S on scale C; read the reciprocal which is 1.25 on scale CI on the reverse side of the rule, keep this number 1.25 in mind and then set the right index of scale C to this number 1.25 on scale LL2 and opposite 5 on scale C read 3.05 on scale LL3, now keep 3.05 in mind and then set runner to this number 23.05 on C; and read the reciprocal .328 on CI which is the answer sought.

It will be noted that in this problem besides various operations of the slide and runner, it was necessary to take two readings mentally and reset the same ou the slide rule7 which may readily cause an cr roi. A

By my new method all that is necessary to solve the above example is to set the lett index ot scale B to 0.8 on scale LL() and opposite on scale B read answer .32S ou scale LLO.

Example 2.

Required log.. .635.

OldA method-set runner to .635 on C; read reciprocal 1.575 on CI, keep this number in mind and set runner to 1.575 on LLZ: read .451ton Dzlog.. l.575.- Taking thc cologarithm gives T546 as the answer. By the new method set the runner to .(535 on scale LLO. read .454 on scale A, this is thc cri-logarithm which deducted trom 0 gives I.546 as the answer.

I claim:

l. In a slide rule having two fixed hars and one sliding bar, a standard logarithmic scale 0n said slidingT 'bar and a log log scale ot decimal quantities on one of said tixed bars so arranged with respect to each other that the hyperbolic co-logarithms of numbers can be read directly from one'to the other.

2. In a slide rule al standard logarithmic scale7 and a. log log scale of vdecimal quan tities. so arranged with respect to each other that the numbers on the log log scale are in alignment with their respective h vperbolic co-logarithms on the standard scale. whereby the Y hyperbolic co-logarithms ot numbers can be read directly from one to the other. l 3. In .a slide rule. a log. log scale of decimal quantities, a standard logarithmic double sca-le, one of the latter scales moveable relative t0 the othenand to the log log scale, the said log log scalevso arranged with respect to the said logarithmic scales, that numbers on the log log scale are in alignment with their respective hyperbolic co-logarithms. on the logarithmic scales` whereby the hyperbolic co-logarithms of numbers can be read directly from one to the other.

In testimony whereof I affix my signature in presence of two witnesses.

ADOLF WV. KEUFFEL.

IVitnesses:

A. F. MENZER, B. B. VAN Siem. 

